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Simplifying (7 + -1b)(5b + -3) = 0 Reorder the terms: (7 + -1b)(-3 + 5b) = 0 Multiply (7 + -1b) * (-3 + 5b) (7(-3 + 5b) + -1b * (-3 + 5b)) = 0 ((-3 * 7 + 5b * 7) + -1b * (-3 + 5b)) = 0 ((-21 + 35b) + -1b * (-3 + 5b)) = 0 (-21 + 35b + (-3 * -1b + 5b * -1b)) = 0 (-21 + 35b + (3b + -5b2)) = 0 Combine like terms: 35b + 3b = 38b (-21 + 38b + -5b2) = 0 Solving -21 + 38b + -5b2 = 0 Solving for variable 'b'. Factor a trinomial. (-7 + b)(3 + -5b) = 0Subproblem 1
Set the factor '(-7 + b)' equal to zero and attempt to solve: Simplifying -7 + b = 0 Solving -7 + b = 0 Move all terms containing b to the left, all other terms to the right. Add '7' to each side of the equation. -7 + 7 + b = 0 + 7 Combine like terms: -7 + 7 = 0 0 + b = 0 + 7 b = 0 + 7 Combine like terms: 0 + 7 = 7 b = 7 Simplifying b = 7Subproblem 2
Set the factor '(3 + -5b)' equal to zero and attempt to solve: Simplifying 3 + -5b = 0 Solving 3 + -5b = 0 Move all terms containing b to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + -5b = 0 + -3 Combine like terms: 3 + -3 = 0 0 + -5b = 0 + -3 -5b = 0 + -3 Combine like terms: 0 + -3 = -3 -5b = -3 Divide each side by '-5'. b = 0.6 Simplifying b = 0.6Solution
b = {7, 0.6}
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